Spencer L. Seager
Michael R. Slabaugh
www.cengage.com/chemistry/seager
Chapter 1:
Matter, Measurements,
and Calculations
Jennifer P. Harris
LEARNING OBJECTIVES/ASSESSMENT
When you have completed your study of this chapter, you should be able
to:
1. Explain what matter is. (Section 1.1; Exercise 1.2)
2. Explain differences between the terms physical and chemical
as applied to:
a. Properties of matter (Section 1.2; Exercises 1.10 b & c)
b. Changes in matter (Section 1.2; Exercises 1.8 a & b)
3. Describe matter in terms of the accepted scientific model.
(Section 1.3; Exercise 1.12)
4. On the basis of observation or information given to you, classify
matter into the correct category of each of the following pairs:
a. Heterogeneous or homogeneous (Section 1.4; Exercise 1.22)
b. Solution or pure substance (Section 1.4; Exercise 1.24)
c. Element or compound (Section 1.4; Exercise 1.18)
5. Recognize the use of measurement units in everyday activities.
(Section 1.5; Exercise 1.28)
6. Recognize units of the metric system, and convert measurements done
using the metric system into
related units. (Section 1.6; Exercises 1.30 and 1.40)
7. Express numbers using scientific notation, and do calculations with
numbers expressed in scientific
notation. (Section 1.7; Exercises 1.48 and 1.60)
8. Express the results of measurements and calculations using the
correct number of significant figures.
(Section 1.8; Exercises 1.64 and 1.66)
9. Use the factor‐unit method to solve numerical problems.
(Section 1.9; Exercise 1.82)
10. Do calculations involving percentages. (Section 1.10; Exercise 1.92)
11. Do calculations involving densities. (Section 1.11; Exercise 1.98)
Topics covered in Chapter One
All sections of Chapter One will be covered.
Example exercises include:
1.7 – 1.17
1.22 – 1.25
1.29 – 1.38
1.46 – 1.75
1.77 – 1.80
1.87 – 1.99
MATTER & MASS
• Matter is anything that has mass and occupies space.
• Mass is a measurement of the amount of matter in an
object.
• Mass is independent of the location of an object.
• An object on the earth has the same mass as the same
object on the moon.
WEIGHT
• Weight is a measurement of the gravitational force acting
on an object.
• Weight depends on the location of an object.
• An object weighing 1.0 lb on earth weighs about 0.17 lb
on the moon.
PHYSICAL & CHEMICAL PROPERTIES
• PHYSICAL PROPERTIES OF MATTER
• Physical properties can be observed or
measured without attempting to change the
composition of the matter being observed.
• Examples: physical state (duh), color, shape
and mass
• CHEMICAL PROPERTIES OF MATTER
• Chemical properties can be observed or
measured only by attempting to change the
matter into new substances.
• Examples: flammability and the ability to
react (e.g. when vinegar and baking soda
are mixed)
PHYSICAL & CHEMICAL CHANGES
• PHYSICAL CHANGES OF MATTER
• Physical changes take place without a
change in composition.
• Examples: changes of state, like
freezing, melting, or evaporation of a
substance (e.g. water)
• CHEMICAL CHANGES OF MATTER
• Chemical changes are always
accompanied by a change in
composition. Most color changes.
• Examples: burning of paper and the
fizzing of a mixture of vinegar and
baking soda
Physical or Chemical Properties?
1.
2.
3.
4.
5.
6.
Color of gold
Tendency of silver to tarnish
Flammability of gasoline
Boiling point of alcohol
Smell of perfume
Different properties of ozone
• Has the formula of O3
• Bluish color
• A gas a room temperature
• Decomposes on exposure to sunlight
Physical or Chemical Changes?
1. Sugar dissolves in hot water
2. Copper metal turns green over time with exposure to air
3. Compressed liquid propane evaporates when the valve is
opened on the container
4. Sugar burns in a pot when heated to a high temperature
PARTICULATE MODEL OF MATTER
• All matter is made up of tiny
particles called molecules and
atoms.
• MOLECULES
• A molecule (or atom, depending
on the substance) is the smallest
particle of a pure substance that
is capable of a stable
independent existence.
• ATOMS
• Atoms are the particles that
make up molecules.
MOLECULE CLASSIFICATION
• Diatomic molecules contain two atoms.
• Triatomic molecules contain three atoms.
• Polyatomic molecules contain many atoms.
MOLECULE CLASSIFICATION (continued)
• HOMOATOMIC MOLECULES
• The atoms contained in homoatomic molecules are of
the same kind.
• HETEROATOMIC MOLECULES
• The atoms contained in heteroatomic molecules are of
two or more kinds.
homoatomic
heteroatomic
MOLECULE CLASSIFICATION EXAMPLE
• Classify the molecules in these diagrams using the terms
diatomic, triatomic, or polyatomic molecules.
• Classify the molecules using the terms homoatomic or
heteroatomic molecules.
CLASSIFICATION OF MATTER
• Matter can be classified into several categories based on
chemical and physical properties.
• PURE SUBSTANCES
• Pure substances have a constant composition and a fixed
set of other physical and chemical properties.
• Example: pure water
(always contains the same
proportions of hydrogen and
oxygen and freezes at a specific
temperature)
CLASSIFICATION OF MATTER (continued)
• MIXTURES
• Mixtures can vary in composition and properties.
• Example: mixture of table sugar and water
(can have different proportions of sugar and water)
• A glass of water could contain one, two, three, etc.
spoons of sugar.
• Properties such as
sweetness would be
different for the mixtures
with different proportions.
HETEROGENEOUS MIXTURES
• The properties of a sample of a heterogeneous mixture
depends on the location from which the sample was taken.
• A pizza pie is a heterogeneous mixture. A piece of crust
has different properties than a piece of pepperoni taken from
the same pie.
HOMOGENEOUS MIXTURES
• Homogeneous mixtures are also called solutions. The
properties of a sample of a homogeneous mixture are the
same regardless of where the sample was obtained from the
mixture.
• Samples taken from any part of a mixture made up of one
spoon of sugar mixed
with a glass of water will
have the same properties,
such as the same taste.
ELEMENTS
• Elements are pure substances that are made up of
homoatomic molecules or individual atoms of the same
kind.
• Examples: oxygen gas made up of homoatomic molecules
and copper metal made up of individual copper atoms
COMPOUNDS
• Compounds are pure substances that are made up of
heteroatomic molecules or individual atoms (ions) of two or
more different kinds.
• Examples: pure water made up of heteroatomic molecules
and table salt made up of sodium atoms (ions) and chlorine
atoms (ions)
MATTER CLASSIFICATION SUMMARY
MATTER CLASSIFICATION EXAMPLE
• Classify H2, F2, and HF using the classification scheme from
the previous slide.
• Solution:
• H2, F2, and HF are all pure substances because they
have a constant composition and a fixed set of physical
and chemical properties.
• H2 and F2 are elements because they are pure
substances composed of homoatomic molecules.
• HF is a compound because it is a pure substance
composed of heteroatomic molecules.
Matter Classification
1. Coffee
2. Apple juice
3. Gold
4. Table salt
5. Methane (CH4)
6. Urine
7. Clean air
8. Pure water
9. Nitrogen gas
10. Concrete
11. Bronze (composed of tin and copper)
12. water and gasoline mixed together
MEASUREMENTS & UNITS
• Measurements consist of two
parts, a number and a unit or
label such as feet, pounds, or
gallons.
• Measurement units are agreed
upon by those making and
using the measurements.
• Measurements are made using
measuring devices (e.g. rulers,
balances, graduated cylinders,
etc.). (Name other common
measuring devices)
METRIC SYSTEM
• The metric system is a decimal system in which larger and
smaller units are related by factors of 10.
• TYPES OF METRIC SYSTEM UNITS
• Basic or defined units [e.g. 1 meter (1 m)] are used to
calculate derived units [e.g. 1 square meter (1 m2)].
• Which of the above are basic units?
THE USE OF PREFIXES
• Prefixes are used to relate basic and derived units.
• The common prefixes are given in the following table:
TEMPERATURE SCALES
• The three most
commonly-used
temperature scales
are the Fahrenheit,
Celsius and Kelvin
scales.
• The Celsius and
Kelvin scales are
used in scientific
work.
TEMPERATURE CONVERSIONS
• Readings on one temperature scale can be converted to the
other scales by using mathematical equations.
• Converting Fahrenheit to Celsius.
5 

C
F  32
9
• Converting Celsius to Fahrenheit.
9 

F
C  32
5
• Converting Kelvin to Celsius.


 

C  K  273
• Converting Celsius to Kelvin.
K   C  273
TEMPERATURE CONVERSION PRACTICE
• Covert 22°C and 54°C to Fahrenheit and Kelvin.

F


9
22  C  32  71.6  F  72  F
5
K  22  C  273  295 K



9
F  54  C  32  129.2  F  129  F
5
K  54  C  273  327 K
COMMONLY USED METRIC UNITS
SCIENTIFIC NOTATION
• Scientific notation provides a convenient way to express
very large or very small numbers.
• Numbers written in scientific notation consist of a product of
two parts in the form M x 10n, where M is a number between
1 and 10 (but not equal to 10) and n is a positive or negative
whole number.
• The number M is written
with the decimal in the
standard position.
SCIENTIFIC NOTATION (continued)
• STANDARD DECIMAL POSITION
• The standard position for a decimal is to the right of the
first nonzero digit in the number M.
• SIGNIFICANCE OF THE EXPONENT n
• A positive n value indicates the number of places to the
right of the standard position that the original decimal
position is located.
• A negative n value indicates
the number of places to
the left of the standard
position that the original
decimal position is located.
Convert to scientific notation
1. 1,000
2. 0.1
3. 10
4. 1
5. 1,016,200
6. 0.0310
7. 0.0000009203
Convert to regular numbers
1. 1.034 X 100
2. 9.02 X 101
3. 2.003 X 10-5
4. 6.023 X 107
More conversions
Put final answer into scientific notation.
1. 12.5 mm into km
2. 3.650 X 108 ng into g
3. 125 uL into mL
Make these changes in exponential numbers
1. 670 X 10-8 = ? X 10-11
2. 0.0475 X 106 = ? X 105
3. 1.25 X 10-3 = ? X 102
SCIENTIFIC NOTATION MULTIPLICATION
• Multiply the M values (a and b) of each number to give a
product represented by M'.
• Add together the n values (y and z) of each number to give a
sum represented by n'.
• Write the final product as M' x 10n'.
• Move decimal in M' to the standard position and adjust n' as
necessary.
a  10 b  10   a  b10 
3.0  10 4.0  10   3.0  4.0 10
y
8
yz
z
-2
 12  10 6
 1.2  10 7
( 8 )( 2 )

SCIENTIFIC NOTATION DIVISION
• Divide the M values (a and b) of each number to give a
quotient represented by M'.
• Subtract the denominator (bottom) n value (z) from the
numerator (top) n value (y) to give a difference represented by
n'.
• Write the final quotient as M' x 10n'.
• Move decimal in M' to the standard position and adjust n' as
necessary.
a  10    a 10 
b  10   b 
y
y-z
z
3.0  10   3.0 10
4.0  10  4.0
8
(8) - (-2)
-2
 0.75  1010
 7.5  10 9

SCI NOTATION ADD/SUBTRACT
• Change the exponential values of numbers involved to be the
same for all numbers.
• Add or subtract (a and b values) in the usual way, the
exponential value doesn’t change
• Write the answer as M' x 10n'.
• Move decimal in M' to the standard position and adjust n' as
necessary.
1.25 X 105 + 4.62 X 104 = 1.25 X 105 + 0.462 X 105 =
1.712 X 105 or 1.71 X 105
SIGNIFICANT FIGURES
• Significant figures are the numbers in a measurement that represent the
certainty of the measurement, plus one number representing an estimate.
• COUNTING ZEROS AS SIGNIFICANT FIGURES
• Leading zeros are never significant figures.
• Buried zeros are always
significant figures.
• Trailing zeros are generally
significant figures.
SIGNIFICANT FIGURES (continued)
Using the apparatus supplied at each station, determine the
measurement with the correct number of significant figures.
SIGNIFICANT FIGURES (continued)
• The answer obtained by multiplication or division must contain
the same number of significant figures (SF) as the quantity
with the fewest number of significant figures used in the
calculation.
4.325  4.5  19.4625  19
4 SF  2 SF 
2 SF
4.325  4.5
 0.961  0.96
4 SF  2 SF 
2 SF
SIGNIFICANT FIGURES (continued)
• The answer obtained by addition or subtraction must contain
the same number of places to the right of the decimal (prd)
as the quantity in the calculation with the fewest number of
places to the right of the decimal.
5.325  5.5  10.825  10.8
3 prd  1prd 
1 prd
5.325  5.5  0.175  0.2
3 prd  1prd 
1 prd
ROUNDING RULES FOR NUMBERS
• If the first of the nonsignificant figures to be dropped from an
answer is 5 or greater, all the nonsignificant figures are
dropped and the last remaining significant figure is increased
by one.
• If the first of the nonsignificant figures to be dropped from an
answer is less than 5, all nonsignificant figures are dropped
and the last remaining significant figure is left unchanged.
Round 10.825 to 1place to the right of the decimal.
⇒10.8
Round −0.175 to 1 place to the right of the decimal.
⇒ −0.2
EXACT NUMBERS
• Exact numbers are numbers that have no uncertainty (they
do not affect significant figures).
• A number used as part of a defined relationship between
quantities is an exact number (e.g. 100 cm = 1 m).
• A counting number obtained by counting individual objects
is an exact number (e.g. 1 dozen eggs = 12 eggs).
• A reduced simple fraction is an exact number (e.g. 5/9 in
equation to convert ºF to ºC).
EXACT NUMBERS
Some exact numbers are defined.
2.54 cm = 1 in (exact numbers)
1 mL = 1 cm3
Calculate the following
Report answers to the correct number of significant figures and
round as appropriate.
1. 89.3 X 77.0 X 0.08 =
2. (7.890 X 1012) / (6.7 X 104) =
3. 67.8 X 9.8 / 100.04 =
4. 89.6 + 98.33 – 4.674 =
5. 0.004 + 0.09879 =
6. (2.45 X 108) + (1.225 X 10-3) =
7. (568.99 – 232.1) X 5.3 =
USING UNITS IN CALCULATIONS
• The factor-unit method for solving numerical problems is a
four-step systematic approach to problem solving.
• Step 1: Write down the known or given quantity. Include both the
numerical value and units of the quantity.
• Step 2: Leave some working space and set the known quantity
equal to the units of the unknown quantity.
• Step 3: Multiply the known quantity by one or more factors, such
that the units of the factor cancel the units of the known quantity
and generate the units of the unknown quantity.
• Step 4: After you generate the desired units of the unknown
quantity, do the necessary arithmetic to produce the final numerical
answer.
SOURCES OF FACTORS
• The factors used in the factor-unit method are fractions
derived from fixed relationships between quantities. These
relationships can be definitions or experimentally measured
quantities.
• An example of a definition that provides factors is the
relationship between meters and centimeters: 1m = 100cm.
This relationship yields two factors:
1m
100 cm
and
100 cm
1m
FACTOR UNIT METHOD EXAMPLES
• A length of rope is measured to be 1834 cm. How many meters is
this?
• Solution: Write down the known quantity (1834 cm). Set the known
quantity equal to the units of the unknown quantity (meters). Use
the relationship between cm and m to write a factor (100 cm = 1 m),
such that the units of the factor cancel the units of the known
quantity (cm) and generate the units of the unknown quantity (m).
Do the arithmetic to produce the final numerical answer.
1834 cm

m
 1m 
1834 cm
  18.34 m
 100 cm 
PERCENTAGE
• The word percentage means per one hundred. It is the
number of items in a group of 100 such items.
• PERCENTAGE CALCULATIONS
• Percentages are calculated using the equation:
part
%
 100
whole
• In this equation, part represents the number of specific items
included in the total number of items.
EXAMPLE PERCENTAGE CALCULATION
• A student counts the money she has left until pay day and
finds she has $36.48. Before payday, she has to pay an
outstanding bill of $15.67. What percentage of her money
must be used to pay the bill?
• Solution: Her total amount of money is $36.48, and the part is
what she has to pay or $15.67. The percentage of her total is
calculated as follows:
part
15.67
%
 100 
 100  42.96%
whole
36.48
DENSITY
• Density is the ratio of the mass of a sample of matter divided
by the volume of the same sample.
mass
density 
volume
or
m
d
v
DENSITY CALCULATION EXAMPLE
• A 20.00 mL sample of liquid is put into an empty beaker that
had a mass of 31.447 g. The beaker and contained liquid
were weighed and had a mass of 55.891 g. Calculate the
density of the liquid in g/mL.
• Solution: The mass of the liquid is the difference between the
mass of the beaker with contained liquid, and the mass of the
empty beaker or 55.891g -31.447 g = 24.444 g. The density
of the liquid is calculated as follows:
m 24.444 g
g
d 
 1.222
v 20.00 mL
mL
Perform the following calculations
Report the final answer using the correct number of significant
figures and rounding as appropriate.
1. convert 22.55 in. into cm.
2. 1760 yds into m. Use 36 in/yd.
3. -40oC into K.
4. -40oC into 0F
5. A possible gold tooth crown has a volume of 1.07 mL and a
mass of 20.6 g. Calculate the density. Is it pure gold?
6. How many minutes does it take to run 10.0 km at a pace of
7.5 mi/hr?
7. How many mL are in 2.0 gallons? Use 4 qts/gal, 2 pints/qt,
16 oz = 1 pint and 29.57 mL = 1 oz.
8. 60.0 g of a solution contains 3.7 g of salt. What is the %
concentration of NaCl?